http://www.slideshare.net/rorycawley/linkedin-oauth-for-curious-people
Some example code to learn more about LinkedIn OAuth. It doesn't use an OAuth library and you can see every step clearly.
I highly advise you do what I did and read the blogs from Khur Boon Kgim.
http://blog.thewebcafes.com/post/1502524959/php-step-by-step-oauth-for-dummies-based-on-linkedin